symbolic way of intimating {36} that a particular factor is absent in a gamete or zygote. Represented thus the zygotic constitution of a pure rose-combed bird is RRpp; for it has been formed by the union of two gametes both of which contained R but not P. Similarly we may denote the pure pea-combed bird as rrPP. On crossing the rose with the pea union occurs between a gamete Rp and a gamete rP, resulting in the formation of a heterozygote of the constitution RrPp. The use of the small letters here informs us that such a zygote contains only a single dose of each of the factors R and P, although, of course, it is possible for a zygote, if made in a suitable way, to have a double dose of any factor. Now when such a bird comes to form gametes a separation takes place between the part of the zygotic cell containing R and the part which does not contain it (r). Half of its gametes, therefore, will contain R and the other half will be without it (r). Similarly half of its gametes will contain P and the other half will be without it (p). It is obvious that the chances of R being distributed to a gamete with or without P are equal. Hence the gametes containing R will be of two sorts, RP and Rp, and these will be produced in equal numbers. Similarly the gametes without R will also be of two sorts, rP and rp, and these, again, will be produced in equal numbers. Each of the hybrid walnut-combed birds, therefore, gives rise to a series consisting of equal numbers of gametes of the four different types RP, Rp, rP, and rp; and the breeding {37} together of such F_1 birds means the bringing together of two such series of gametes. When this happens an ovum of any one of the four types has an equal chance of being fertilised by a spermatozoon of any one of the four types. A convenient and simple method of demonstrating what happens under such circumstances is the method sometimes termed the "chessboard" method. For two series each consisting of four different types of gamete we require a square divided up into 16 parts. The four terms of the gametic series are first written horizontally across the four sets of four squares, so that the series is repeated four times. It is then written vertically four times, care being taken to keep to the same order. In this simple mechanical way all the possible combinations are represented and in their proper proportions.